Incentive constraints in games with bounded memory

In this paper I analyze a repeated coordination game between a bounded memory player and a fully rational player. A bounded memory player is a player who is subject to imperfect recall, but, conditional on this constraint, acts optimally every point in time given her beliefs over the actual history of the game. I show that the results contrast with the ones in the finite automata literature. In particular, a result denoted the “tyranny of the weak” in Gilboa and Samet (Games Econ Behav 1: 213–221, 1989) is no longer present here.     

The bounded core for games with precedence constraints

An element of the possibly unbounded core of a cooperative game with precedence constraints belongs to its bounded core if any transfer to a player from any of her subordinates results in payoffs outside the core. The bounded core is the union of all bounded faces of the core, it is nonempty if the core is nonempty, and it is a continuous correspondence on games with coinciding precedence constraints. If the precedence constraints generate a connected hierarchy, then the core is always nonempty. It is shown that the bounded core is axiomatized similarly to the core for classical cooperative games, namely by boundedness (BOUND), nonemptiness for zero-inessential two-person games (ZIG), anonymity, covariance under strategic equivalence (COV), and certain variants of the reduced game property (RGP), the converse reduced game property (CRGP), and the reconfirmation property. The core is the maximum solution that satisfies a suitably weakened version of BOUND together with the remaining axioms. For games with connected hierarchies, the bounded core is axiomatized by BOUND, ZIG, COV, and some variants of RGP and CRGP, whereas the core is the maximum solution that satisfies the weakened version of BOUND, COV, and the variants of RGP and CRGP.     

Numerical methods for portfolio selection with bounded constraints

This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Homotopy method for solving variational inequalities with bounded box constraints

In this paper, using the Gabriel–Moré smoothing function of the median function, a smooth homotopy method for solving nonsmooth equation reformulation of bounded box constrained variational inequality problem VIP(l,u,F$l,u,F$) is given. Without any monotonicity condition on the defining map F$F$, for starting point chosen almost everywhere in Rⁿ$R^n$, existence and convergence of the homotopy pathway are proven. Nevertheless, it is also proven that, if the starting point is chosen to be an interior point of the box, the proposed homotopy method can also serve as an interior point method.     

Optimum maneuvers of a skip vehicle with bounded lift constraints

This paper presents the analytical solutions of the problem of optimum maneuvering of a glide vehicle flying in the hypervelocity regime. The investigation is based on the approximation of Allen and Eggers; namely, that along the fundamental part of a reentry or ascent trajectory, the aerodynamic forces greatly exceed the components of the gravitational force in the directions tangent and normal to the flight path.The problem consists of finding an optimal control law for the lift such that the final velocity or the final altitude is maximized. This problem can be viewed as bringing the vehicle to the best condition for interception, penetration, or making an evasive maneuver.If the range is free, the optimal lift control is obtained in closed form. If the lift control is bounded, then bounded control is optimal whenever it is reached. The switching sequences for different cases are discussed, and it is shown that there are at most two switchings. Bounded lift control is always at the ends of the optimal trajectory; for the case of two switchings, the optimal trajectory has an inflection point.The authors wish to thank the National Aeronautics and Space Administration for the Grant No. NGR-06-003-033 under which this work was carried out.     

On the differentiability of optimal values for bounded nonlinear programs with equality constraints

We consider a parametrized family of nonlinear programs where the feasible region is defined by equality constraints in a ball. The global optimal value is shown to be twice continuously differentiable over an open and dense set in the perturbation parameter space.     

将预算弱势变为优势

面对预算,作为财务总监的你,是兴奋、乐观、干劲十足,还是头疼、无奈、缺乏信心？根据Centage公司和管理及行政学院（IOMA）的调查,最糟糕的是由于不完善的预算编制进程造成的预算不准确,从而明显降低相关各方对预算的信心。     

Immersions with bounded curvature

This article proves that the immersions of compact manifolds into a fixed compact Riemannian manifold, with bounds on the second fundamental forms and either the diameter or volume of the induced metrics, fall into only finitely many topological types.     

Diversity analysis in multiple-choice questionnaires

We extend the analysis of the diversity of questionnaires with binary (yes–no) answers to the case of questionnaires with multiple answers. It has been demonstrated that the original techniques used by Khmaladze (2009) are universal and can be applied to prove limit theorems for more general cases. It was shown that this different framework again leads us to a model similar to that for a large number of rare events that Khmaladze obtained in Khmaladze (2009), namely, to the so called Karlin–Rouault law.     

Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry

We study the class ofn-Riemannian manifolds in the title such that the torsion elements in the fundamental group have a definite bound on their orders. Our main result asserts the existence of a kind of generalized Seifert fiber structure onM ⁿ , for which the fundamental group of fibers injects into that ofM ⁿ . This provides a necessary and sufficient topological condition for a manifold to admit a sufficiently collapsed metric in our class. Among other consequences we obtain a strengthened version of the gap conjecture in this context.The work of the first author is partially supported by NSF Grant DMS 9303999. The work of the second author is supported by MSRI through NSF grant DMS 9022140 and partially supported by NSF Grant DMS 9204095.     

The multiple-choice multi-period knapsack problem

This paper introduces the multiple-choice multi-period knapsack problem in the interface of multiple-choice programming and knapsack problems. We first examine the properties of the multiple-choice multi-period knapsack problem. A heuristic approach incorporating both primal and dual gradient methods is then developed to obtain a strong lower bound. Two branch-and-bound procedures for special-ordered-sets type 1 variables that incorporate, respectively, a special algorithm and the multiple-choice programming technique are developed to locate the optimal solution using the above lower bound as the initial solution. A computer program written in IBM's APL2 is developed to assess the quality of this lower bound and to evaluate the performance of these two branch-and-bound procedures.     

存在借贷资金的随机资金预算问题研究

讨论了企业运用自有资金及银行贷款进行投资时的资金预算问题,与以往的研究不同,本文假设投资支出、年投资收益以及银行贷款都为随机变量,而且,文章的研究并不要求待选的投资项目具有相同的投资期或具有相同的寿命周期.给出了随机环境下净现值收益的期望值模型及期望值目标规划模型,并设计了基于随机模拟的遗传算法,给出了模型的一般解决方法,此外,还提供了两个数值例子,用以说明建模思想,并例证算法的有效性.     

Operators with bounded conjugation orbits

For a bounded invertible operator on a complex Banach space let be the set of operators in for which Suppose that and is in A bound is given on in terms of the spectral radius of the commutator. Replacing the condition in by the weaker condition as for every 0$">, an extension of the Deddens-Stampfli-Williams results on the commutant of is given.

     

Spanning trees with bounded degrees

Lets andk be positive integers. We prove that ifG is ak-connected graph containing no independent set withks+2 vertices thenG has a spanning tree with maximum degree at mosts+1. Moreover ifs3 and the independence number (G) is such that (G)1+k(s–1)+c for some0ck thenG has a spanning tree with no more thanc vertices of degrees+1.